QuantLib_OneFactorStudentCopula (3) - Linux Man Pages

NAME

QuantLib::OneFactorStudentCopula - One-factor Double Student t-Copula.

SYNOPSIS

#include <ql/experimental/credit/onefactorstudentcopula.hpp>

Inherits QuantLib::OneFactorCopula.

Public Member Functions

OneFactorStudentCopula (const Handle< Quote > &correlation, int nz, int nm, Real maximum=10, Size integrationSteps=200)

Real density (Real m) const
Density function of M.
Real cumulativeZ (Real z) const
Cumulative distribution of Z.

Detailed Description

One-factor Double Student t-Copula.

The copula model [ Y_i = a_i,M+qrt{1-a_i^2}:Z_i ]

is specified here by setting the probability density functions for \$ Z_i \$ (\$ D_Z \$) and \$ M \$ (\$ D_M \$) to Student t-distributions with \$ N_z \$ and \$ N_m \$ degrees of freedom, respectively.

The variance of the Student t-distribution with \$ \$ degrees of freedom is \$ / ( - 2) \$. Since the copula approach requires zero mean and unit variance distributions, variables \$ Z \$ and \$ M \$ are scaled by \$ qrt{(N_z - 2) / N_z} \$ and \$ qrt{(N_m - 2) / N_m}, \$ respectively.

Possible enhancements

Improve performance/accuracy of the calculation of inverse cumulative Y. Tabulate and store it for selected correlations?

Member Function Documentation

Real density (Real m) const [virtual]

Density function of M.

Derived classes must override this method and ensure zero mean and unit variance.

Implements OneFactorCopula.

Real cumulativeZ (Real z) const [virtual]

Cumulative distribution of Z.

Derived classes must override this method and ensure zero mean and unit variance.

Implements OneFactorCopula.

Author

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